The proton nuclear spin-lattice relaxation times and self-diffusion coefficients of ethane and propane were measured at elevated temperatures and pressures. It is found that pure ethane and propane depart from the linear correlations between relaxation time and viscosity/temperature and diffusivity found for pure higher alkanes and dead crude oils. The inverse relationship between the diffusion coefficient and viscosity/temperature for pure methane, pure higher alkanes, and methane-higher alkane mixtures holds for pure ethane and propane. The proton relaxation times were calculated and compared with the experimental data for ethane. The governing relaxation mechanism is shown to be the spin rotation interaction in gaseous ethane. At liquid densities, intra- and intermolecular dipole-dipole interactions and the spin rotation interaction all have significant contributions. A mixing rule was developed to estimate T 1 of gas mixtures. The estimated results by the mixing rule compared closely with experimental results for CH4-CO2 and CH 4-N2 gas mixtures. T1 and T 2 relaxation times of about 30 heavy crude oils were measured with different frequency NMR spectrometers. In addition, relaxation times of some oil samples were measured at various temperatures. Light oils have equal T 1 and T2 relaxation times. However, heavy or asphaltene crude oils have different T1 and T2 with the ratio of T1/ T2 increasing with increasing viscosity, Larmor frequency, asphaltene content and free radical content. For heavy oils, apparent T2 time constants increase and the signal amplitude decreases with increasing echo spacing. Apparent hydrogen index of heavy crude oils increases with increasing temperature. With increasing echo spacing, apparent hydrogen index of heavy oils decreases.